$94$ people attended a baseball game. Everyone there was a fan of either the home team or the away team. The number of home team fans was $38$ less than $2$ times the number of away team fans. How many home team and away team fans attended the game?
Explanation: Let $x$ equal the number of home team fans and $y$ equal the number of away team fans. The system of equations is then: ${x+y = 94}$ ${x = 2y-38}$ Solve for $x$ and $y$ using substitution. Since $x$ has already been solved for, substitute ${2y-38}$ for $x$ in the first equation. ${(2y-38)}{+ y = 94}$ Simplify and solve for $y$ $ 2y-38 + y = 94 $ $ 3y-38 = 94 $ $ 3y = 132 $ $ y = \dfrac{132}{3} $ ${y = 44}$ Now that you know ${y = 44}$ , plug it back into ${x = 2y-38}$ to find $x$ ${x = 2}{(44)}{ - 38}$ $x = 88 - 38$ ${x = 50}$ You can also plug ${y = 44}$ into ${x+y = 94}$ and get the same answer for $x$ ${x + }{(44)}{= 94}$ ${x = 50}$ There were $50$ home team fans and $44$ away team fans.